Phase-resolved functional optical coherence tomography: simultaneous imaging of the stokes vectors, structure, blood flow velocity, standard deviation and birefringence in biological samples

ABSTRACT

A phase-resolved functional optical coherence tomography system simultaneously obtains the Stokes vectors, structure, blood flow velocity, standard deviation, and birefringence images in human skin. The multifunctional images were obtained by processing the analytical interference fringe signals derived from the two perpendicular polarization detection channels. The blood flow velocity and standard deviation images were obtained by comparing the phase from the pairs of analytical signals in the neighboring A-lines in the same polarization state. The Stokes vectors were obtained by processing the analytical signals from two polarization diversity detection channels for the same reference polarization state. From the four Stokes vectors, the birefringence image, which is insensitive to the orientations of the optical axis in the sample, was obtained. Multifunctional images of a port wine stain birthmark in human skin are demonstrated.

RELATED APPLICATIONS

[0001] The present application is related to U.S. Provisional PatentApplication serial No. 60/371,204, filed on Apr. 9, 2002, which isincorporated herein by reference and to which priority is claimedpursuant to 35 USC 119.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention relates to the field of phase-resolved functionaloptical coherence tomography systems and in particular to systems whichcan obtain the Stokes vectors, structure, blood flow velocity, standarddeviation, and birefringence images in tissue.

[0004] 2. Description of the Prior Art

[0005] Optical coherence tomography (OCT) is a noninvasive, noncontactimaging modality that uses coherent gating to obtain high-resolutioncross-sectional images of tissue microstructure. OCT is analogous toultrasound imaging except that infrared light waves rather than acousticwaves are used. Consequently, the spatial! resolution of OCT is morethan an order of magnitude better than that of the ultrasound. OCT wasfirst used clinically in ophthalmology for the imaging and diagnosis ofretinal disease. Recently, OCT has been applied to imaging subsurfacestructure in human skin, blood vessels, oral cavity and the respiratory,urogenital, and GI tracts.

[0006] Several extensions of OCT have been developed for functionalimaging of tissue physiology. For example, optical Doppler tomography(ODT) combines the Doppler principle with coherence gating fortomographic imaging of tissue microstructure and blood flowsimultaneously. See Nelson, et al., “Method And Apparatus For OpticalDoppler Tomographic Imaging Of Fluid Flow Velocity In Highly ScatteringMedia,” U.S. Pat. No. 5,991,697 (1999), which is incorporated herein byreference. Polarization sensitive OCT (PS-OCT) combines polarizationsensitive detection with OCT to determine tissue birefringence. See DeBoer, et al., “Birefringence Imaging In Biological Tissue UsingPolarization Sensitive Optical Coherent Tomography,” U.S. Pat. No.6,208,415 (2001), which is incorporated herein by reference. Bothtechniques use the phase information from the interference fringes toobtain additional physiologically important information. Although anumber of potential clinical applications of ODT and PS-OCT have beendemonstrated, to date, ODT and PS-OCT imaging have been performed usingseparate systems. However, there are many clinical indications wheredetermination of both blood perfusion and tissue birefringence isimportant. For example, in burn injuries both the loss of cutaneousblood perfusion and changes in tissue birefringence are two criticalfactors used to determine burn depth. Simultaneous imaging of thechanges in blood perfusion and collagen birefringence by functional OCT(F-OCT) will according to the invention allow better clinical managementof burn injuries.

BRIEF SUMMARY OF THE INVENTION

[0007] A phase-resolved functional optical coherence tomography systemis disclosed below that can simultaneously obtain the Stokes vectors,structure, blood flow velocity, standard deviation, and birefringenceimages of human skin. The multifunctional images were obtained byprocessing the analytical interference fringe signals derived from thetwo perpendicularly or independently polarized detection channels. Theblood flow velocity, and standard deviation images were obtained bycomparing the phase from the pairs of analytical signals in theneighboring A-lines in the same polarization state. The Stokes vectorswere obtained by processing the analytical signals from two polarizationdiversity detection channels for the same reference polarization state.From the four Stokes vectors, the birefringence image, which isinsensitive to the orientations of the optical axis in the sample, wasobtained. Images of structure, flow, standard deviation, phaseretardation, and Stokes vectors can be obtained and displayedsimultaneously.

[0008] The invention is thus defined as an apparatus for phase-resolvedfunctional optical coherence tomography of a sample characterized byoptical birefringence comprising an interferometer having a source arm,a reference arm, a sample arm and a detector arm. A source of at leastpartially coherent polarized light is coupled to the source arm. Thepartially coherent polarized light is characterized by a well definedpolarization state. A polarization modulator is provided, so thatpolarization modulated light is returned to the detector arm. Polarizedlight is incident on the sample and arbitrarily polarized light isreturned to the detector arm from the sample arm according to samplebirefringence. The returned light from the reference arm and sample arminterfere in the detector arm to form polarization interference fringes.A phase modulator is coupled to the interferometer for modulating anoptical path length difference between the reference and sample arms ofthe interferometer at a predetermined phase modulation frequency. Ascanner is coupled to the interferometer for scanning the sample. Asensor is coupled to the interferometer for detecting backscatteredradiation received by the interferometer from the scanner to detectinterference fringes within the interferometer. A polarizationdemodulator demodulates the polarization interference fringes togenerate a complete polarization state description of the backscatteredlight from the sample by preserving phase relationships betweenorthogonal components of the polarization interference fringes formedfrom backscattered light from the sample and from the reference arm. Adata processor is coupled to the sensor for processing signals from thesensor corresponding to the interference fringes established by thebackscattered radiation in the interferometer and controls the scannerto generate tomographic images. The data processor simultaneouslygenerates the Stokes vectors, and generates tomographic structure, bloodflow velocity, standard deviation, and birefringence images at eachpixel in the image.

[0009] The tomographic images are composed of data from A-line scans ofthe sample in a given polarization state of the light impinging on thesample. The tomographic blood flow velocity and standard deviationimages are generated by the data processor by comparing the phase frompairs of analytical signals in the neighboring A-lines in the samepolarization state.

[0010] The sensor has two polarization diversity detection channels andthe tomographic Stokes vector images are generated by the data processorby processing the analytical signals from the two polarization diversitydetection channels for the same reference polarization state. Thetomographic birefringence image is generated by the data processor fromthe four Stokes vectors.

[0011] The polarization modulator controls the polarization state oflight in the reference arm, which rapidly varies between statesorthogonal in the Poincare sphere at a predetermined frequency to insurethat birefringence measurements are independent of orientations of theoptical axis of the sample. The sensor detects four states of lightpolarization at each pixel. The data processor controls the scanner tosequentially perform a predetermined number of lateral line scans,A-line scans, for each polarization state. The data processor generatesDoppler frequency shift (f_(n)) and standard deviation σ_(n) values atthe nth pixel with complex analytical signals from the four sequentialA-scans. The data processor generates an average of the Dopplerfrequency shift (f_(n)) and standard deviation σ_(n) values at the nthpixel for each polarization state to generate tomographic Doppler shiftand variance images.

[0012] The sensor detects two orthogonal polarization diversitychannels, and the data processor generates the coherence matrixtherefrom to generate the Stokes vectors characterizing the polarizationstate of the backscattered light, and the light intensity. The dataprocessor generates the Stokes vectors according to: $\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{S_{0,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} + {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}} \\{S_{1,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} - {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}}\end{matrix} \\{S_{2,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Re}\left\lbrack \quad {{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}} \right\rbrack}}}}}\end{matrix} \\{S_{3,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Im}\left\lbrack \quad {{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)} \right\rbrack}}}}}\end{matrix} & \quad\end{matrix}$

[0013] where {tilde over (Γ)}_(j) ^(H)(t_(m)) and {tilde over (Γ)}^(V)_(j)(t_(m)) are the complex signals detected from the two orthogonalpolarization channels at axial rime t_(m) for the jth A-scan, {tildeover (Γ)}_(j) ^(H*)(t_(m)) and {tilde over (Γ)}^(V*) _(j)(t_(m)) aretheir conjugates. The data processor generates the structural image fromaveraging the Stokes vectors for the four states of light polarization.The data processor generates the phase retardation image from S₀, whichcharacterizes the birefringence distribution in the sample by therotation of the Stokes vectors in the Poincare sphere.

[0014] The invention further includes a method performed by the abovecombination of elements. In particular the invention includes a methodof performing phase-resolved F-OCT to simultaneous image the Stokesvectors, structural, Doppler frequency shift, standard deviation, andbirefringence of a sample comprising the steps of scanning the sample;performing PS-OCT while scanning each pixel location; simultaneouslyperforming ODT while scanning each pixel location; determining theStokes vectors at each pixel location; and generating the tomographicstructural, Doppler frequency shift, standard deviation, andbirefringence images of the sample.

[0015] The method further comprising the step of averaging in thegeneration of the Doppler frequency shift and standard deviation toreduce the influence of speckle noise and tissue birefringenceartifacts.

[0016] While the apparatus and method has or will be described for thesake of grammatical fluidity with functional explanations, it is to beexpressly understood that the claims, unless expressly formulated under35 USC 112, are not to be construed as necessarily limited in any way bythe construction of “means” or “steps” limitations, but are to beaccorded the full scope of the meaning and equivalents of the definitionprovided by the claims under the judicial doctrine of equivalents, andin the case where the claims are expressly formulated under 35 USC 112are to be accorded full statutory equivalents under 35 USC 112. Theinvention can be better visualized by turning now to the followingdrawings wherein like elements are referenced by like numerals.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1 is a simplified block diagram of the F-OCT system of theinvention.

[0018]FIG. 2 is a synchronizing time clock diagram for the system ofFIG. 1.

[0019]FIG. 3 is an example of the data output of the system of FIG. 1showing the simultaneous imaging of the Stokes vectors, structure, bloodflow velocity, standard deviation and birefringence information from invivo human skin. The top four panels are the Stokes vector imagescorresponding to the four reference polarization states. The bottom fourpanel images are: A: structural image; B: blood flow velocity image; C:standard deviation image; and D: phase retardation image.

[0020] The invention and its various embodiments can now be betterunderstood by turning to the following detailed description of thepreferred embodiments which are presented as illustrated examples of theinvention defined in the claims. It is expressly understood that theinvention as defined by the claims may be broader than the illustratedembodiments described below.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021] In the illustrated embodiment, we describe a phase-resolved F-OCTsystem that can simultaneously obtain the Stokes vectors, structure,blood flow velocity, standard deviation, and birefringence images inhuman skin or tissue. The system is based on a phase-resolved signalprocessing method whereby the multifunctional images were obtained byprocessing the analytical interference fringe signals derived from twoperpendicular polarization detection channels.

[0022] The fiber-based high-speed F-OCT system for multifunctionalimaging is shown in the diagrammatic depiction of FIG. 1. A 1300 nmpartially coherent broadband light source 10 manufactured by AFCTechnologies with a full-width-half-maximum (FWHM) bandwidth of 80 nmwas used as the light source. A visible light source, such as asemiconductor laser 11 is used as an aiming source, but otherwise playsno significant role in the data imaging. Source 10 and laser 11 arecombined by means of a 2×1 coupler 13 and provided as input to apolarizer 15. In the illustrated embodiment polarizer 15 linearlypolarizes the light provided to a 2×2 fiber splitter 12. Light enteringsplitter 12 is divided between a sample arm 14 and a reference arm 16 ofthe Michelson interferometer, generally denoted by reference numeral 18.

[0023] In the reference arm 16 a rapid scanning optical delay (RSOD)line 20 is aligned such that only group delay scanning at 500 Hz isgenerated without phase modulation. RSOD line 20 is conventional and isgenerally described in Tearney et.al., Opt. Lett. 22, 1811 (1997) andRollins et.al., Optics Express 3, 219 (1998). A stable phase modulationat 500 kHz is generated using an E-O modulator 22 for heterodynedetection. Phase modulator 22 in reference arm 16 is driven by functiongenerator 48, which in turn is controlled by a general purpose interfacebus 56 (GPIB) from a data acquisition (DAQ) board in computer 54.Function generator 48 generates a TRIGGER OUT signal communicated online 64 to computer 54 for arming the DAQ board. The galvanometer inRSOD 20 is similarly driven by a scan driver generator 59 coupled tofunction generator 50 which in turn is coupled to bus 56 and generates asynchronization signal, SYN OUT, which is provided on line 58 tocomputer 54 for driving the galvanometer scanner in RSOD 20.Polarization modulator 24 in sample arm 14 is driven by high voltageamplifier 60, which in turn is controlled by function generator 46coupled to bus 56 and TRIGGER IN signal communicated from computer 54 online 62.

[0024] A probe 26 with a collimator and infinity-corrected objectivedriven by a translation stage or stage controller 28 is employed in thesample arm 14 to scan sample 30. Stage controller 28 is coupled to line62, TRIGGER IN. The backscattered light is transmitted throughpolarization modulator 24 through coupler 12 to polarization control 68to polarization beam splitter 66. Polarization control 68 is amechanically adjustable fiber loop polarizer, which serves to equalizethe amount of light in each of two orthogonal polarization states sentto polarization beam splitter 66, which has been received in thedetector arm from reference arm 16. The backscattered light signal orfringe signals from the two polarization channels are separated bypolarization beam splitter 66 and detected by two photo-detectors 334and 32, then high pass filtered, amplified and digitized by a 12-bit,analogue-to-digital conversion board 36/38 (dual-channel, 5M samples perchannel, National Instruments).

[0025] Polarization modulator 24 is used to control the polarizationstate of light in the sample arm 14, which rapidly varied between statesorthogonal in the Poincare sphere at 125 Hz. In the illustratedembodiment, polarization modulator 24 is driven to provide in sequencefour linearly independent polarization states corresponding to the fourStokes vectors. For example, the four linearly independent polarizationstates may be vertically and horizontally linearly polarized light andclockwise and counterclockwise circularly polarized light, or any otherfour linearly independent polarization states as may be desired. Thechoice of orthogonal polarization states in the Poincare sphere isimportant because it insures the birefringence measurements will beindependent of orientations of the optical axis in the sample 30. Inorder to measure the Stokes vectors accurately, four states of lightpolarization are generated for each lateral location. For eachpolarization state, four A-line scans are performed sequentially.Therefore, a total of 16 A-line scans are used to calculate the Stokesvectors, phase retardation, structure, Doppler mean frequency, andDoppler standard deviation images simultaneously.

[0026] Also, if polarization modulator 24 is controlled to provide thefour Stokes vectors, the Mueller matrix of sample 30 may be measured.For example, $\begin{pmatrix}S_{0}^{\prime} \\S_{1}^{\prime} \\S_{2}^{\prime} \\S_{3}^{\prime}\end{pmatrix} = {\begin{pmatrix}M_{11} & M_{12} & M_{13} & M_{14} \\M_{21} & M_{22} & M_{23} & M_{24} \\M_{31} & M_{32} & M_{33} & M_{34} \\M_{41} & M_{42} & M_{43} & M_{44}\end{pmatrix}\begin{pmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{pmatrix}}$

[0027] where $\begin{pmatrix}S_{0}^{\prime} \\S_{1}^{\prime} \\S_{2}^{\prime} \\S_{3}^{\prime}\end{pmatrix}$

[0028] is the Stokes vector after reflection from sample 30,$\begin{pmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{pmatrix}$

[0029] is the Stokes vector incident on sample 30 and $\begin{pmatrix}M_{11} & M_{12} & M_{13} & M_{14} \\M_{21} & M_{22} & M_{23} & M_{24} \\M_{31} & M_{32} & M_{33} & M_{34} \\M_{41} & M_{42} & M_{43} & M_{44}\end{pmatrix}$

[0030] is the Mueller matrix. By providing through control ofpolarization modulator 24 light having the pure Stokes vectors S₀, S₁,S₂ and S₃ incident on sample 30, the elements of the Mueller matrix, canbe readily derived in computer 54, i.e. for${S = {S_{0} = \begin{pmatrix}1 \\0 \\0 \\0\end{pmatrix}}},$

[0031] then $S^{\prime} = \begin{pmatrix}M_{11} \\M_{21} \\M_{31} \\M_{41}\end{pmatrix}$

[0032] and similarly for each of the other Stokes vectors S₁, S₂ and S₃.

[0033] The synchronizing time clock diagram is shown in FIG. 2. Channel1 on line 42 is the signal generated nom the synchronized TRIGGER OUTfrom function generator 46, and it arms the A-to-D conversion incomputer 54. Channel 2 on line 52 is the signal generated by functiongenerator 48 to control the polarization modulator 24. Channel 3 on line44 is the triangle signal from the function generator 50 to control thegalvanometer scanning. Channel 4 on line 40 is the signal generated bySYN OUT of function generator 50 through a digital delay. This signal isused to trigger the phase modulation and data acquisition.

[0034] The positive slope of the signal shown on line 40 acts as atrigger to start the phase modulation signal generation and dataacquisition. The negative slope acts as a trigger to stop the phasemodulation signal generation and data acquisition. The negative slope ofthis signal triggers the start of polarization modulation signalgeneration. The data acquisition (DAQ) is ready for the four states oflight polarization when the TRIGGER OUT signal in line 42 has a negativeslope. Line 44 is the triangle signal driving the galvanometer scannerwhich is RSOD 20. The driving signals for the polarization statemodulator 24, phase modulator 22 and galvanometer scanner in the RSOD 20are all generated from bus signals by the three function generators 46,48 and 50. The translation stage 28 is controlled by bus 56 so that itmoves one pixel when the signal in line 52 of FIG. 2 has run four steps.

[0035] Because Doppler and polarization sensitive detection requiresphase information, we first calculate the complex analytical signal{tilde over (Γ)}(t) of the interference fringe using Hilbert transform$\begin{matrix}{{\overset{\sim}{\Gamma}(t)} = {{\Gamma (t)} + {\frac{i}{\pi}P{\int_{- \infty}^{\infty}{\frac{\Gamma \left( t^{\prime} \right)}{t^{\prime} - t}\quad {t^{\prime}}}}}}} & (1)\end{matrix}$

[0036] Where P denotes the Cauchy principle value. Because theinterference signal ┌(t) is quasi-monochromatic, the complex analyticalsignal is given by: $\begin{matrix}{{\overset{\sim}{\Gamma}(t)} = {2{\int_{0}^{\infty}{\int_{- T}^{T}{{\Gamma \left( t^{\prime} \right)}{\exp \left( {{- 2}\quad {\pi }\quad v\quad t^{\prime}} \right)}\quad {t^{\prime}}{\exp \left( {2\quad {\pi }\quad v\quad t} \right)}\quad {v}}}}}} & (2)\end{matrix}$

[0037] The digital approach to determine the complex analytical signalusing Hilbert transformation is shown in the following block diagram

┌(t)→FFT→×H(v)→band pass filter→FFT ⁻¹→{tilde over (Γ)}(t)

[0038] where FFT denotes the fast Fourier transform, x is a multiplyingsymbol and H(v) is the Heaviside function given by: $\begin{matrix}{{H(v)} = \begin{Bmatrix}0 & {v < 0} \\1 & {v \geq 0}\end{Bmatrix}} & (3)\end{matrix}$

[0039] and FFT⁻¹ denotes the inverse fast Fourier transform.Multiplication of the Heaviside function is equivalent to performing anoperation that discards the spectrum in the negative frequency region.

[0040] For each polarization state, four sequential A-scans areperformed. The Doppler frequency shift (f_(n)) and standard deviationσ_(n) values at the nth pixel can be calculated with complex analyticalsignals from the four sequential A-scans: $\begin{matrix}{f_{n} = {\frac{1}{2\quad \pi \quad T}{\tan^{- 1}\left( \frac{{Im}\left( {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{3}\quad {{{\overset{\sim}{\Gamma}}_{j}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j + 1}^{*}\left( t_{m} \right)}}}} \right)}{{Re}\left( {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{3}\quad {{{\overset{\sim}{\Gamma}}_{j}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j + 1}^{*}\left( t_{m} \right)}}}} \right)} \right)}}} & (4) \\{\sigma^{2} = {\frac{1}{2\quad \pi^{2}T^{2}}\left( {1 - \frac{{\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{3}\quad {{{\overset{\sim}{\Gamma}}_{j}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j + 1}^{*}\left( t_{m} \right)}}}}}{\frac{1}{2}\left( {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{3}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{*}\left( t_{m} \right)}} + {{{\overset{\sim}{\Gamma}}_{j + 1}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j + 1}^{*}\left( t_{m} \right)}}} \right\rbrack}} \right)}} \right)}} & (5)\end{matrix}$

[0041] where {tilde over (Γ)}_(j)(t_(m)) and {tilde over(Γ)}*_(j)(t_(m)) are the complex signals at axial time t_(m)corresponding to the jth A-scan and its conjugate respectively, {tildeover (Γ)}_(j+1)(t_(m)) and {tilde over (Γ)}*_(j+1)(t_(m)) are thecomplex signals at axial time t_(m) corresponding to the next A-scan andits conjugate, respectively, T is the time duration between A-scans, andM is an even number that denotes the window size in the axial directionfor each pixel. This algorithm also effectively reduces speckle noise.The calculated Doppler frequency shifts and standard deviation valuesfrom each polarization state is then averaged to obtain Doppler shiftand variance images.

[0042] For every polarization state controlled by the polarizationmodulator 24, the A-scan signals corresponding to the two orthogonalpolarization diversity channels were digitized. Considering thequasi-monochromatic light beam, the coherence matrix can be calculatedfrom the complex electrical field vector from these two channels:$\begin{matrix}{J = {\begin{pmatrix}{\langle{{E_{H}^{*}(t)}{E_{H}(t)}}\rangle} & {\langle{{E_{H}^{*}(t)}{E_{V}(t)}}\rangle} \\{\langle{{E_{V}^{*}(t)}{E_{H}(t)}}\rangle} & {\langle{{E_{V}^{*}(t)}{E_{V}(t)}}\rangle}\end{pmatrix} = \begin{pmatrix}J_{HH} & J_{HV} \\J_{VH} & J_{VV}\end{pmatrix}}} & (6)\end{matrix}$

[0043] where E_(H), and E_(v) are the components of the complex electricfield vector corresponding to the horizontal and vertical polarizationchannels, respectively, and E*_(H), and E*_(V) are their conjugates,respectively. The Stokes vector can be derived from the coherencematrix:

S ₀ =J _(HH) +J _(W)

S ₁ =J _(HH) −J _(W)

S ₂ =J _(HV) +J _(VH)

S ₃ =i(J _(VH) −J _(HV))   (7)

[0044] where S₀, S₁, S₂, and S₃ are the four components of the Stokesvector. S₁, S₂, and S₃ are the coordinates of the Stokes vector in thePoincare sphere characterizing the polarization state of thebackscattered light, and S₀ is the module of the Stokes vectorcharacterizing light intensity. The Stokes vector for the nth pixel andone state of light polarization can be calculated as: $\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{S_{0,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} + {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}} \\{S_{1,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} - {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}}\end{matrix} \\{S_{2,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Re}\left\lbrack \quad {{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}} \right\rbrack}}}}}\end{matrix} \\{S_{3,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Im}\left\lbrack \quad {{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)} \right\rbrack}}}}}\end{matrix} & (8)\end{matrix}$

[0045] where {tilde over (Γ)}_(j) ^(H)(t_(m)) and {tilde over (Γ)}^(V)_(j)(t_(m)) are the complex signals detected from the two orthogonalpolarization channels at axial rime t_(m) for the jth A-scan, {tildeover (Γ)}_(j) ^(H*)(t_(m)) and {tilde over (Γ)}^(V*) _(j)(t_(m)) aretheir conjugates. From the Stokes vectors for the four states of lightpolarization the structural image is obtained by averaging the four. S₀,the phase retardation image, which characterizes the birefringencedistribution in the sample, is calculated by the rotation of the Stokesvectors in the Poincare sphere.

[0046] We have used our phase-resolved F-OCT system to perform in vivoimaging of a port wine stain birthmark in human skin. The simultaneousimaging of the Stokes vectors, structure, blood flow, velocity, standarddeviation, and birefringence is shown in the collection of data imageswhich comprise FIG. 3. The image area is 2 mm×1.5 mm. The top four,columnar panels are the Stokes vectors corresponding to the fourdifferent, polarization states shown in FIG. 2. From left to right, theyare S₀, S₁, S₂, and S₃, respectively, obtained by averaging four A-linesin every polarization state. The bottom row of images are structure,Doppler frequency shift (blood flow velocity), standard deviation, andbirefringence images. Implementation of the polarization diversitydetection in the intensity, Doppler and standard deviation imagessignificantly reduces the artifact due to tissue birefringence. Inaddition, speckle noise is also greatly reduced. The greater detailnoted in the structure image as compared to the So image indicates thatthe speckle noise is greatly reduced when polarization diversitydetection is used. Small vessels can be clearly identified in theDoppler frequency shift and standard deviation images. The arrows in theDoppler frequency shift and standard deviation images indicate that theblood vessels are located approximately 500 μm below the skin surface.The nonuniform birefringence of human skin can also be identified in thephase retardation image.

[0047] In summary, we have developed a phase-resolved F-OCT systemcapable of simultaneous imaging of the Stokes vectors, structure,Doppler frequency shift, standard deviation, and birefringence bycombining PS-OCT and ODT. The detection scheme we implemented in ourF-OCT system allows polarization diversity averaging in the detection ofthe Doppler frequency shift and standard deviation, which greatlyreduces the influence of speckle noise and tissue birefringenceartifacts. Given the noninvasive nature and exceptional high spatialresolution, phase-resolved F-OCT that can simultaneously provide tissuestructure, blood perfusion, and birefringence information has greatpotential for both basic biomedical research and clinical medicine.

[0048] While it is recognized that optical coherence tomography (OCT) isa non-invasive technique that images tissue structure up to a depth of 2mm with spatial resolution of 10 μm. We have extended the capability ofOCT with optical Doppler tomography (ODT), which measures depth resolvedflow in tissue, and polarization sensitive OCT (PS-OCT), which measuresdepth resolved polarization changes of reflected light.

[0049] These three imaging modalities give functional information,namely structure, flow and polarization, in biological tissues and havea wide range of applications in medicine, which include: determinationof burn depth; guidance regarding the optimal depth for burn debridementprior to definitive closure; imaging and diagnosis of corneal andretinal pathology; diagnosis and treatment of tumors in thegastrointestinal and respiratory tracts, cervix, and skin; monitoring oftissue perfusion and viability immediately after injury, wound closure,replantation, or microvascular reconstruction; optimized radiationdosimetry by assessing and quantifying alterations in tissuemicrovascular and matrix structure; determination of long-termalterations in microvascular hemodynamics and morphology in chronicdiseases such as diabetes mellitus and arteriosclerosis; and mapping ofconical hemodynamics with high spatial resolution for brain research.

[0050] The critical challenge in burn treatment is to assess the depthof the thermal injury accurately in order to determine whether the burncan heal spontaneously or whether surgical intervention is required;because of the thin and complex nature of human skin, burn depthvariations on the order of 100 μm can make the difference betweenspontaneous epithelial regeneration or surgical intervention with skingrafting. This decision is particularly crucial on cosmetically andfunctionally important areas such as the face and hands where the skinis 1-2 mm thick.

[0051] There are two critical factors in burn depth determination due tothermal damage: (1) loss of cutaneous blood circulation, and (2) changesin tissue structure. Tissue perfusion introduces a Doppler shift onreflected light. Experiments with fluorescein fluorometry and laserDoppler flowmetry (LDF) have demonstrated that the cutaneousmicrocirculation plays a crucial role in determining whether a burn canheal spontaneously through epithelial regeneration. The birefringence ofcollagen in human skin changes the polarization state of light. Thermaldenaturation, which occurs between 56-65° C. reduces birefringence bychanging the collagen from a rod-like to a random coil structure.PS-OCT/ODT measures spatially resolved changes in the polarization stateand Doppler shift of light reflected from human skin up to a depth of1-2 mm with 10-30 μm resolution. Changes in blood perfusion and collagenbirefringence due to thermal denaturation can be used for burn depthdetermination in human skin.

[0052] Information provided by PS-OCT/ODT can be important during allstages of burn wound management. Preoperatively, the burn surgeon candecide on one of two possible treatment plans for casualties with burninjuries: (a) concentrate on supporting the patient while the burn woundevolves and wound healing begins; or (b) immediate burn debridement withskin grafting. Intraoperatively, PS-OCT/ODT provides guidance regardingthe optimal depth for burn debridement prior to definitive closure.Postoperatively, PS-OCT/ODT can be used to monitor physiologicallysignificant healing events including neovascularization. The potentialto rapidly and accurately image and distinguish viable from nonviabletissue over large areas and at different depths is of enormous benefitto the attending burn surgeon.

[0053] Ocular blood flow and retinal nerve fiber layer thicknessdetermination is also an area of application of the invention. Oculardisease can have a devastating impact on a patient's quality of life.Because the uninterrupted optical pathway allows direct visualobservation of nervous and vascular tissue, the eye provides animportant indicator of not only ophthalmologic but also systemicvascular and neurologic disease. Much ocular pathology involvesdisturbances in blood flow, including diabetic retinopathy, low tensionglaucoma, anterior ischemic optic neuritis, and macular degeneration.For example, in diabetic retinopathy, retinal blood flow is reduced andthe normal autoregulatory capacity deficient. Ocular hemodynamics arealtered in patients with glaucoma and severe loss of visual function hasbeen associated with reduced macular blood flow.

[0054] Polarization and Doppler shift sensitive depth-resolvedmeasurements of light reflected from the retina can be used to determinethe retinal nerve fiber layer (NFL) thickness and retinal perfusion withhigh sensitivity and spatial resolution simultaneously.

[0055] In summary, the range of applications of the invention includes:

[0056] Cancer diagnosis in the gastrointestinal (GI), respiratory, andurogenital tracts (including larynx, bladder, uterine_cervix etc.).

[0057] Cancer/diagnosis in skin

[0058] Diagnosis of cardiovascular disease

[0059] Generation of an in situ three-dimensional tomographic image andvelocity profiles of blood-perfusion in human skin at discrete spatiallocations in either the superficial or deep dermis;

[0060] Burn depth determination; provide guidance regarding the optimaldepth for burn debridement prior to definitive closure;

[0061] Determination of tissue perfusion and viability immediately afterinjury, wound closure, replantation, or transposition of eitherrotational or free skin flaps;

[0062] Evaluation of the vascular status of a buried muscle flap coveredby a split thickness skin graft; perfusion in the superficial and deeperflap components can be monitored separately;

[0063] Distinguishing between arterial or venous occlusion and determinethe presence and/or extent of adjacent post-traumatic arterial or venousvascular injury by providing an situ tomographic image and velocityprofile of blood flow;

[0064] Monitoring the effects of pharmacological intervention on skinmicrocirculation (e.g., effects of vasoactive compounds or inflammatorymediators; determination of transcutaneous drug penetration kinetics;evaluation of the potency of penetration enhancers; irritation ofchemical compounds, patch-test allergens and ultraviolet radiation;comparison of the reactivity of the skin microcirculation in differentage and ethnic groups);

[0065] Determination of the extent of intestinal vascular insufficiencyor infarction; to conserve intestine by confining resection tononvascularized segments;

[0066] Measurement of ocular, blood flow and birefringence, diagnosis ofocular disease;

[0067] Imaging of three-dimensional tumor microvasculature forangiogenesis research;

[0068] Optimizing radiation dosimetry by assessing and quantifyingalterations in tissue microvascular and matrix structure;

[0069] Determining long-term alterations in microvascular hemodynamicsand morphology in chronic diseases such as diabetes mellitus andarteriosclerosis;

[0070] Mapping cortical hemodynamics with high spatial resolution forbrain research;

[0071] Guiding surgical procedures for brain surgery

[0072] Finally, phase resolved F-OCT with axicon lens is also attractivefor the following industrial applications:

[0073] Imaging flow dynamics in microchannels of micro-electro-mechanicsystem (MEMS) chips.

[0074] Characterizing and monitoring of flow velocity when the fluid isencapsulated in highly scattering materials such as fibrous substancesor resin composites;

[0075] Accurately measuring particle concentration and size, and fluidflow velocity profile and providing useful diagnostic information forprocess monitoring and quality control;

[0076] Monitoring in situations involving turbid fluid flow samples suchas materials processing of paints, pigmented fluids, and other types ofopaque liquids; and

[0077] Characterizing and monitoring of dry particulate flow withinconduits such as a jet stream; here, a significant advantage of DOT isthat the flow could be characterized and “monitored without disturbingthe stream.

[0078] Many alterations and modifications may be made by those havingordinary skill in the art without departing from the spirit and scope ofthe invention. Therefore, it must be understood that the illustratedembodiment has been set forth only for the purposes of example and thatit should not be taken as limiting the invention as defined by thefollowing claims. For example, notwithstanding the fact that theelements of a claim are set forth below in a certain combination, itmust be expressly understood that the invention includes othercombinations of fewer, more or different elements, which are disclosedin above even when not initially claimed in such combinations.

[0079] The words used in this specification to describe the inventionand its various embodiments are to be understood not only in the senseof their commonly defined meanings, but to include by special definitionin this specification structure, material or acts beyond the scope ofthe commonly defined meanings. Thus if an element can be understood inthe context of this specification as including more than one meaning,then its use in a claim must be understood as being generic to allpossible meanings supported by the specification and by the word itself.

[0080] The definitions of the words or elements of the following claimsare, therefore, defined in this specification to include not only thecombination of elements which are literally set forth, but allequivalent structure, material or acts for performing substantially thesame function in substantially the same way to obtain substantially thesame result. In this sense it is therefore contemplated that anequivalent substitution of two or more elements may be made for any oneof the elements in the claims below or that a single element may besubstituted for two or more elements in a claim. Although elements maybe described above as acting in certain combinations and even initiallyclaimed as such, it is to be expressly understood that one or moreelements from a claimed combination can in some cases be excised fromthe combination and that the claimed combination may be directed to asubcombination or variation of a subcombination.

[0081] Insubstantial changes from the claimed subject matter as viewedby a person with ordinary skill in the art, now known or later devised,are expressly contemplated as being equivalently within the scope of theclaims. Therefore, obvious substitutions now or later known to one withordinary skill in the art are defined to be within the scope of thedefined elements.

[0082] The claims are thus to be understood to include what isspecifically illustrated and described above, what is conceptionallyequivalent, what can be obviously substituted and also what essentiallyincorporates the essential idea of the invention.

We claim:
 1. An apparatus for phase-resolved functional opticalcoherence tomography of a sample characterized by optical birefringencecomprising: an interferometer having a source arm, a reference arm, asample arm and a detector arm; a source of at least partially coherentpolarized light coupled to the source arm, the partially coherentpolarized light being characterized by a well defined polarizationstate; a polarization modulator for providing modulated polarized lightof selected linearly independent polarization states incident on thesample, wherein backscattered arbitrarily polarized modulated light isreturned to the detector arm from the sample arm according to samplebirefringence, the returned light from the reference arm and sample arminterfering in the detector arm to form polarization interferencefringes; a phase modulator coupled to the interferometer for modulatingan optical path length difference in the reference and sample arms ofthe interferometer at a predetermined phase modulation frequency; ascanner coupled to the interferometer for scanning the sample; a sensorcoupled to the interferometer for detecting backscattered radiationreceived by the interferometer from the scanner to detect interferencefringes within the interferometer; and a polarization demodulator todemodulate the polarization interference fringes; and a data processorcoupled to the sensor for processing signals from the sensorcorresponding to the interference fringes established by thebackscattered radiation in the interferometer and for controlling thescanner to generate tomographic images to generate a completepolarization state description of the backscattered light from thesample by preserving phase relationships between orthogonal componentsof the polarization interference fringes formed from backscattered lightfrom the sample and from the reference arm, and wherein the dataprocessor simultaneously generates the Stokes vectors, and generatestomographic structure, blood flow velocity, standard deviation, andbirefringence images at each pixel in the image.
 2. The apparatus ofclaim 1 where the tomographic images are composed of data from A-linescans of the sample in each of the polarization states of the lightimpinging on the sample, and where the tomographic blood flow velocityand standard deviation images are generated by the data processor bycomparing the phase from pairs of analytical signals in the neighboringA-lines in the same polarization state.
 3. The apparatus of claim 1where the sensor has two polarization diversity detection channels andwhere the tomographic Stokes vector images are generated by the dataprocessor by processing the analytical signals from the two polarizationdiversity detection channels for the same reference polarization state.4. The apparatus of claim 3 where the tomographic birefringence image isgenerated by the data processor from the four Stokes vectors.
 5. Theapparatus of claim 1 where the polarization modulator controls thepolarization state of light in the sample arm, which rapidly variesbetween states orthogonal in the Poincare sphere at a predeterminedfrequency to insure that birefringence measurements are independent oforientations of the optical axis of the sample.
 6. The apparatus ofclaim 1 where the sensor detects four polarization states of light ateach pixel.
 7. The apparatus of claim 6 where the data processorcontrols the scanner to sequentially perform a predetermined number oflateral line scans, A-line scans, for each polarization state.
 8. Theapparatus of claim 7 where the data processor generates Dopplerfrequency shift (f_(n)) and standard deviation σ_(n) values at the nthpixel with complex analytical signals from the four sequential A-scans.9. The apparatus of claim 8 where the data processor generates anaverage of the Doppler frequency shift (f_(n)) and standard deviationσ_(n) values at the nth pixel for each polarization state to generatetomographic Doppler shift and variance images.
 10. The apparatus ofclaim 1 where the sensor detects two orthogonal polarization diversitychannels, and where the data processor generates the coherence matrixtherefrom to generate the Stokes vectors characterizing the polarizationstate of the backscattered light, and the light intensity.
 11. Theapparatus of claim 10 where the data processor generates the Stokesvectors according to: $\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{S_{0,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} + {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}} \\{S_{1,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} - {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}}\end{matrix} \\{S_{2,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Re}\left\lbrack \quad {{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}} \right\rbrack}}}}}\end{matrix} \\{S_{3,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Im}\left\lbrack \quad {{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)} \right\rbrack}}}}}\end{matrix} & \quad\end{matrix}$

where {tilde over (Γ)}_(j) ^(H)(t_(m)) and {tilde over (Γ)}^(V)_(j)(t_(m)) are the complex signals detected from the two orthogonalpolarization channels at axial rime t_(m) for the jth A-scan, {tildeover (Γ)}_(j) ^(H*)(t_(m)) and {tilde over (64 )}^(V*) _(j)(t_(m)) aretheir conjugates.
 12. The apparatus of claim 1 where the data processorgenerates the structural image from averaging the Stokes vectors for thefour states of light polarization.
 13. The apparatus of claim 1 wherethe data processor generates the phase retardation image from S₀, whichcharacterizes the birefringence distribution in the sample by therotation of the Stokes vectors in the Poincare sphere.
 14. The apparatusof claim 1 where the polarization modulator provides light havingselected Stokes vectors and where the sensor senses the elements of theMueller matrix which are computed in the data processor.
 15. Theapparatus of claim 14 where the polarization modulator provides lighthaving pure states of each of the selected Stokes vectors so that theMueller matrix is directly measured.
 16. A method of performingphase-resolved F-OCT to simultaneous image the Stokes vectors,structural, Doppler frequency shift, standard deviation, andbirefringence of a sample comprising: scanning the sample; performingPS-OCT while scanning each pixel location; simultaneously performing ODTwhile scanning each pixel location; determining the Stokes vectors ateach pixel location; and generating the tomographic structural, Dopplerfrequency shift, standard deviation, and birefringence images of thesample.
 17. The method of claim 16 further comprising averaging in thegeneration of the Doppler frequency shift and standard deviation toreduce the influence of speckle noise and tissue birefringenceartifacts.
 18. A method for performing phase-resolved functional opticalcoherence tomography of a sample characterized by optical birefringencecomprising: providing at least partially coherent polarized light in thesource arm of an interferometer, the partially coherent polarized lightbeing characterized by a well defined polarization state; polarizationmodulating the light in a plurality of linearly independent polarizationstates; phase modulating the light to generate a modulated optical pathlength difference in the reference and sample arms of the interferometerat a predetermined phase modulation frequency; scanning the sample withthe polarization and phase modulated light; returning the polarizationand phase modulated light to a detector arm in the interferometer from areference arm in the interferometer, returning the polarization andphase modulated light to a detector arm in the interferometer from asample arm in the interferometer, where arbitrarily polarized and phaseshifted light is returned to the detector arm from the sample armaccording to sample birefringence and Doppler reflections from flowingfluid in the sample; interfering the returned light from the referencearm and sample arm in the detector arm to form polarization and phaseinterference fringes; detecting the polarization and phase interferencefringes from the backscattered radiation; and processing the detectedsignals from the sensor corresponding to the interference fringesestablished by the backscattered radiation in the interferometer and togenerate a complete polarization state description of the backscatteredlight from the sample by preserving phase relationships betweenorthogonal components of the polarization interference fringes formedfrom backscattered light from the sample and from the reference arm, andwherein the data processor simultaneously generates the Stokes vectors,and generates tomographic structure, blood flow velocity, standarddeviation, and birefringence images at each pixel in the image.
 19. Themethod of claim 18 where processing the detected signals processes datafrom A-line scans of the sample in each of the polarization states ofthe light impinging on the sample, and generates the tomographic bloodflow velocity and standard deviation images by comparing the phase frompairs of analytical signals in the neighboring A-lines in the samepolarization state.
 20. The method of claim 18 where detecting thepolarization and phase interference fringes detects two polarizationdiversity detection channels and where processing the detected signalsgenerates the tomographic Stokes vector images by processing theanalytical signals from the two polarization diversity detectionchannels for the same reference polarization state.
 21. The method ofclaim 20 where generating the four Stokes vectors generates thetomographic birefringence image.
 22. The method of claim 18 wherepolarization modulating the light modulates the polarization state oflight in the sample arm, which rapidly varies between states orthogonalin the Poincare sphere at a predetermined frequency to insure thatbirefringence measurements are independent of orientations of theoptical axis of the sample.
 23. The method of claim 18 where detectingthe polarization and phase interference fringes detects four states oflight polarization at each pixel.
 24. The method of claim 23 wherescanning the sample comprises sequentially scanning a predeterminednumber of lateral line scans, A-line scans, for each polarization state.25. The method of claim 24 where processing the detected signalsgenerates Doppler frequency shift (f_(n)) and standard deviation σ_(n)values at the nth pixel with complex analytical signals from the foursequential A-scans.
 26. The method of claim 25 where processing thedetected signals generates an average of the Doppler frequency shift(f_(n)) and standard deviation σ_(n) values at the nth pixel for eachpolarization state to generate tomographic Doppler shift and varianceimages.
 27. The method of claim 18 where detecting the polarization andphase interference fringes detects two orthogonal polarization diversitychannels, and where processing the detected signals generates thecoherence matrix therefrom to generate the Stokes vectors characterizingthe polarization state of the backscattered light, and the lightintensity.
 28. The method of claim 27 where processing the detectedsignals generates the Stokes vectors according to: $\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{S_{0,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} + {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}} \\{S_{1,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}\left\lbrack \quad {{{{\overset{\sim}{\Gamma}}_{j}^{H}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}} - {{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V^{*}}\left( t_{m} \right)}}} \right\rbrack}}}\end{matrix} \\{S_{2,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Re}\left\lbrack \quad {{{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)}{{\overset{\sim}{\Gamma}}_{j}^{V}\left( t_{m} \right)}} \right\rbrack}}}}}\end{matrix} \\{S_{3,n} = {\sum\limits_{m = {n - {M/2}}}^{n + {M/2}}\quad {\sum\limits_{j = 1}^{4}{2\quad {{Im}\left\lbrack \quad {{\overset{\sim}{\Gamma}}_{j}^{H^{*}}\left( t_{m} \right)} \right\rbrack}}}}}\end{matrix} & \quad\end{matrix}$

where {tilde over (Γ)}_(j) ^(H)(t_(m)) and {tilde over (Γ)}^(V)_(j)(t_(m)) are the complex signals detected from the two orthogonalpolarization channels at axial rime t_(m) for the jth A-scan, {tildeover (Γ)}_(j) ^(H*)(t_(m)) and {tilde over (Γ)}^(V*) _(j)(t_(m)) aretheir conjugates.
 29. The method of claim 18 where processing thedetected signals generates the structural image from averaging theStokes vectors for the four states of light polarization.
 30. The methodof claim 18 where processing the detected signals generates the phaseretardation image from S₀, which characterizes the birefringencedistribution in the sample by the rotation of the Stokes vectors in thePoincare sphere.
 31. The method of claim 18 where polarizationmodulating the light comprises modulating the light to assume acharacterization selected Stokes vectors and where the processing thedetected signals generates the elements of the Mueller matrix.
 32. Theapparatus of claim 31 where modulating the light to assume acharacterization selected Stokes vectors provides light having purestates of each of the selected Stokes vectors so that the Mueller matrixis directly measured.